Electronic origin of magnetic and orbital ordering in insulating LaMnO3

We derive a spin-orbital model for insulating ${\mathrm{LaMnO}}_3$ which fulfills the SU(2) symmetry of $S=2\mathrm{}$ spins at ${\mathrm{Mn}}^{3+}$ ions. It includes the complete $e_g$ and $t_{2g}$ superexchange which follows from a realistic ${\mathrm{Mn}}^{2+}$ multiplet structure in cubic site symmetry, and the Jahn-Teller-induced orbital interactions. We show that the magnetic ordering observed in ${\mathrm{LaMnO}}_3$ is stabilized by a purely electronic mechanism due to the $e_g$ superexchange alone, and provides a unique and quantitatively correct explanation of the observed transition temperature and the anisotropic exchange interactions.